Related papers: Forced kink of $\lambda \phi ^4$ mode
We study the elasticity of the collision of two kinks with an incoming low speed $v\in (0,1)$ for the nonlinear wave equation in dimension $1+1$ known as the $\phi^{6}$ model. We prove for any $k\in\mathbb{N}$ that if the incoming speed $v$…
A topological mechanism is a zero elastic-energy deformation of a mechanical structure that is robust against smooth changes in system parameters. Here, we map the nonlinear elasticity of a paradigmatic class of topological mechanisms onto…
Sine-Gordon kinks are a much studied integrable system that possesses multi-soliton solutions. Recent studies on sine-Gordon kinks with space-dependent square-well-type potentials have revealed interesting dynamics of a single kink…
In this paper, we study the single kink and the kink-antikink collisions of a nonlinear beam equation bearing a fourth-derivative term. We numerically explore some of the key characteristics of the single kink both in its standing wave and…
We give a sufficient condition, in the spirit of Kowalczyk-Martel-Munoz-Van Den Bosch \cite{KMMvdB21AnnPDE}, for the local asymptotic stability of kinks under odd perturbations. In particular, we allow the existence of quite general…
Kinks (or domain walls) are localized transitions between distinct ground states associated with a topological invariant, and are central to many phenomena across physics, from condensed matter to cosmology. While phonon (i.e.,…
An individual defect in a nematic liquid crystal moves not only in response to its interaction with other defects but also in response to an external field. We analyze the motion of a wedge disclination in the presence of an applied field…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate…
A one dimensional trap model for a thermally activated classical particle is introduced to simulate driven dynamics in presence of "ageing" effects. The depth of each trap increases with the time elapsed since the particle has fallen into…
An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…
We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is…
Recently a linearized perturbation theory has been formulated for soliton sectors of quantum field theories. While it is more economical than alternative formalisms, such as collective coordinates, it is currently limited to solitons which…
We consider a real scalar field equation in dimension 1+1 with an even, positive self-interaction potential having two non-degenerate zeros (vacua) 1 and -1. Such a model admits non-trivial static solutions called kinks and antikinks. We…
In the present work we construct kink solutions for different (parabolic and wave) variants of the fractional $\phi^4$ model, in both the sub-Laplacian and super-Laplacian setting. We establish existence and monotonicity results (for the…
In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…
We consider the interaction of solitary waves in a model involving the well-known $\phi^4$ Klein-Gordon theory, but now bearing both Laplacian and biharmonic terms with different prefactors. As a result of the competition of the respective…
The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady…
Thermodynamic description of a model system with magnetoelastic coupling is presented. The elastic, vibrational, electronic and magnetic energy contributions are taken into account. The long-range RKKY interaction is considered together…
We consider the motion of a particle in a random isotropic force field. Assuming that the force field arises from a Poisson field in $\mathbb{R}^d$, $d \geq 4$, and the initial velocity of the particle is sufficiently large, we describe the…